to help pay for art school, kaitlin borrowed money from her credit union. she took out a personal, amortized…

to help pay for art school, kaitlin borrowed money from her credit union. she took out a personal, amortized loan for $53,500, at an interest rate of 5.55%, with monthly payments for a term of 15 years. for each part, do not round any intermediate computations and round your final answers to the nearest cent. if necessary, refer to the list of financial formulas. (a) find kaitlins monthly payment. $ (b) if kaitlin pays the monthly payment each month for the full term, find her total amount to repay the loan. $ (c) if kaitlin pays the monthly payment each month for the full term, find the total amount of interest she will pay. $

to help pay for art school, kaitlin borrowed money from her credit union. she took out a personal, amortized loan for $53,500, at an interest rate of 5.55%, with monthly payments for a term of 15 years. for each part, do not round any intermediate computations and round your final answers to the nearest cent. if necessary, refer to the list of financial formulas. (a) find kaitlins monthly payment. $ (b) if kaitlin pays the monthly payment each month for the full term, find her total amount to repay the loan. $ (c) if kaitlin pays the monthly payment each month for the full term, find the total amount of interest she will pay. $

Answer

Explanation:

Step1: Identify loan - related values

Principal amount $P = 53500$, annual interest rate $r=5.55%=0.0555$, number of years $t = 15$, number of payments per year $n=12$.

Step2: Calculate the monthly interest rate

$i=\frac{r}{n}=\frac{0.0555}{12}=0.004625$.

Step3: Calculate the number of payments

$m = n\times t=12\times15 = 180$.

Step4: Use the amortized - loan payment formula

The formula for the monthly payment of an amortized loan is $M=\frac{P\times i\times(1 + i)^m}{(1 + i)^m-1}$. Substitute the values: $M=\frac{53500\times0.004625\times(1 + 0.004625)^{180}}{(1 + 0.004625)^{180}-1}$. First, calculate $(1 + 0.004625)^{180}\approx2.31777$. Then, $53500\times0.004625 = 247.4375$. $247.4375\times2.31777\approx573.57$. $2.31777-1 = 1.31777$. $M=\frac{573.57}{1.31777}\approx435.24$.

Step5: Calculate the total amount to repay

The total amount to repay $A = M\times m$. $A=435.24\times180 = 78343.20$.

Step6: Calculate the total interest paid

The total interest paid $I=A - P$. $I=78343.20-53500=24843.20$.

Answer:

(a) $$435.24$ (b) $$78343.20$ (c) $$24843.20$